SIL subsystem architecture & test strategy

Models a SIF as an arbitrary chain of series subsystems (sensor / logic solver / final element and beyond) with voting architectures including 1oo2D, then reports the spurious-trip rate and searches for the proof-test interval that meets a PFDavg target — matching how a real SIF is actually assembled and maintained.

• The SIF has more than one subsystem in series (e.g. transmitter + PLC + valve), each with its own voting and failure data.
• A redundant final element or logic solver uses 1oo2D voting and needs its diagnostics credited correctly.
• Weighing a safety upgrade's cost in spurious/nuisance trips against its PFDavg benefit.
• Deciding how often to proof-test, or whether partial-stroke testing between proof tests is worth crediting.

Series subsystems sum PFDavg, each first capped at its own architectural constraint; 1oo2D is quantified with Hokstad-form conservative-bound math cross-checked against an independent numerical Markov model; the proof-test optimizer performs a search over test interval to hit a PFDavg target.